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New research has proven that prime numbers don't just disappear
as numbers get larger — instead, there is an infinite number of
prime numbers separated by a distance of at most 70 million.

The new proof, accepted this month for publication in the journal
Annals of Mathematics, takes the field one step closer to solving
the twin prime conjecture, a famous mathematical idea that
suggests the existence of an infinite number of prime
numbers separated by a distance of 2 (for example, the prime
numbers 11 and 13, which are separated by 2). Prime numbers are
those that are divisible by only themselves and 1.

Prior to this discovery, mathematicians suspected there were
infinitely many twin primes, or prime numbers separated by two,
but proofs hadn't set bounds on how far apart primes could be
separated. [ The
9 Most Massive Numbers in Existence ]

"It's a huge step forward in terms of showing that there are
primes close together," said Daniel Goldston, a mathematician at
San Jose State University in California. "It's a big huge step
toward the twin prime conjecture."

Other mathematicians also applauded the achievement, and its
author, Yitang Zhang, a mathematician unknown in the field.
"Basically, no one knows him," said Andrew Granville, a number
theorist at the Université de Montréal, as
quoted by the Simons Foundation. "Now, suddenly, he has
proved one of the great results in the history of number theory."

In the 1800s, mathematician Alphonse de Polignac noticed a
strange trend in
prime numbers. Though so-called twin primes get less common
as numbers get bigger, de Polignac became convinced that there
were infinitely many twin primes.

But proving it was another matter.

These problems "are very attractive to people because the
problems themselves are not difficult to understand, but the
solution — the proof — could be very difficult," said Zhang of
the University of New Hampshire.

Many attempts relied on finding primes using sieve methods, which
essentially involves crossing out numbers that have larger and
larger factors to find primes (for instance, crossing out all the
numbers divisible by 2, then 3, then 5, then 7, and so on).

All of the small primes can be manually calculated, and if
numbers get large enough,
mathematicians can generalize the technique. But in between
small numbers and big ones is a vast terrain where primes are too
big calculate with the sieve, but too small to make
generalizations about.

In 2005, Daniel Goldston, a mathematician at San Jose State
University in California, and his colleagues János Pintz and Cem
Yildirim developed a new method (called GPY) to make claims for
that middle range of numbers in order to prove that the numerical
gaps between prime numbers are bounded, and not infinite.

"Our method got right up to the point where you would approach
getting this bounded gaps result, but we couldn't get it,"
Goldston said.

Crossing the gap

Zhang had been trying to find a way to close the gap in the GPY
method for years. But last summer, he felt a breakthrough was
close and devoted all his efforts to cracking the prime problem.

He finally developed set of new mathematical methods and used
them to overcome the gap in prior work.

The math community hasn't thoroughly scrutinized the proof to
ensure it's airtight, but several mathematicians in the field
have done a first-pass check and found the logic sound.

The current known maximum gap between primes is 70 million, but
that number may come down dramatically with further iterations of
the proof.